{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WJ5OK5MFZ6KVRQ3HGZXTG5RULP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"912a52c0952a49f12eb3a4abf8913626c495aa72604e2927002e2fd97effde94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T17:50:43Z","title_canon_sha256":"9017bf3a9d1bd12c73cd00e8eccb4b7bf82a0897ec76870673f4c48257c43411"},"schema_version":"1.0","source":{"id":"1803.00528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00528","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00528v1","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00528","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"WJ5OK5MFZ6KV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WJ5OK5MFZ6KVRQ3H","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WJ5OK5MF","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:eef6b931c63c18117bd45b0349ba06f7d0156b7c7bc046fd0a467cebde640759","target":"graph","created_at":"2026-05-18T00:22:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The purpose of this work is twofold. First we study the solutions of a Hamilton-Jacobi equation of the form $u_t(t,x)+\\mathcal{H}(t,x,\\nabla_H u(t,x))=0$, where $\\nabla_H u$ represents the horizontal gradient of a function $u$ defined on the Heisenberg group ${I\\!\\!H}$. Motivated by the recent paper by Liu, Manfredi and Zhou (\\cite{LiMaZh2016}), we prove a Lipschitz continuity preserving property for $u$ with respect to the Kor\\'anyi homogeneous distances $d_G$ in ${I\\!\\!H}$. Secondly, we are keenly interested in introducing the game theory in ${I\\!\\!H}$, taking into account its Sub-Riemannian","authors_text":"Andrea Calogero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T17:50:43Z","title":"Differential games and Hamilton-Jacobi equations in the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00528","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:db43a6131bd91d295ceb6bc005f8647de3c726c627beb8a3b533d754322b35c0","target":"record","created_at":"2026-05-18T00:22:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"912a52c0952a49f12eb3a4abf8913626c495aa72604e2927002e2fd97effde94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T17:50:43Z","title_canon_sha256":"9017bf3a9d1bd12c73cd00e8eccb4b7bf82a0897ec76870673f4c48257c43411"},"schema_version":"1.0","source":{"id":"1803.00528","kind":"arxiv","version":1}},"canonical_sha256":"b27ae57585cf9558c367366f3376345bc5c723825a695e80f6737ad5f148ec0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27ae57585cf9558c367366f3376345bc5c723825a695e80f6737ad5f148ec0e","first_computed_at":"2026-05-18T00:22:11.513935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:11.513935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"raQeprYjIf6lkKnexAJIGZxa3z5lwy9K4itbAZvnKnyU2RjhRXhVF/q9Ezuhj437lfqBFxaPq6StROZf8KSkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:11.514585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db43a6131bd91d295ceb6bc005f8647de3c726c627beb8a3b533d754322b35c0","sha256:eef6b931c63c18117bd45b0349ba06f7d0156b7c7bc046fd0a467cebde640759"],"state_sha256":"851796126cee33e1a250abad70fa5dc2925b4804debcf91a49bcc0f1ae04f929"}